Methods for imaging an object emitting photons suffer from a number of limitations, especially in the case where the object is a human patient, or a section of the patient. The photon emitter is typically a radiopharmaceutical that is injected into, or inhaled by, the patient. In order to minimize deleterious effects on the patient, the quantity of photon emitter, the time during which the emitter is active, and the number of photons emitted, all need to be minimal. Furthermore, detected, detection systems for the photons typically have minimal or no focusing ability. Common detection systems may rely on the equivalent of a fly's eye detection system, wherein the photons are collimated along tubular channels before detection. As one amongst a number of further complications, the object being imaged is typically three-dimensional, but if a collimator is used the detection system has at best only a very approximate way of determining from where, along an axis or within a cone of view of the collimator, a detected single photon has been emitted.
Geometric factors for fly's eye collimators may be calculated. In a paper by Metz et al., entitled “The Geometric transfer function component for scintillation camera collimators with straight parallel holes,” Phys. Med. Biol., 1980, v. 25, p. 1059-1070, the authors develop a method for predicting a geometric transfer function component for conventional scintillation camera collimators. The paper is incorporated herein by reference. In U.S. Pat. No. 6,943,355, to Shwartz, et al., whose disclosure is incorporated herein by reference, a method is described that enables a collimator to usefully detect photons from incident angles exceeding 5°.
Thus, geometric factors may be allowed for, given a scan time that is sufficiently long. However, the scan time is critical, since the long scan time needed by the imaging system means that the patient is exposed for the same long time. Unfortunately, raw data produced by operating at shorter times, or with reduced concentrations of radioactivity to produce the same benefit, has a lower signal to noise ratio than at the longer times. This acquired raw data is insufficient to enable a good reconstruction of local concentrations of the radiopharmaceutical, which is the goal of the imaging system, so that reconstructed images at the shorter times or with reduced concentrations are of extremely low quality.
Regularization, i.e., reformulation of the raw data, may be used to derive images from the raw data. For example, U.S. Pat. Nos. 5,912,993, 6,353,688, and 6,490,374 to Puetter et al., whose disclosures are incorporated herein by reference, describe methods for planar image reconstruction using “Pixon” elements and bases, which are respectively defined as indivisible units of information and sets of possible functions from which the elements are selected.
Wavelet theory may also be used for regularization as described, for example, by Mallat, in a paper entitled “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pat. Anal. Mach. Intell., vol. 11, pp. 674-693, 1989, and by Simoncelli et al., in a paper entitled, “Noise removal via Bayesian wavelet coring,” 3rd IEEE Int'l. Conf. Image Processing, Lausanne, Switzerland, September 1996, vol. 1, pp. 379-382, IEEE Sig. Proc. Society. Both of these papers assume a Laplacian wavelet distribution. A paper entitled, “Wavelet thresholding via a Bayesian approach,” by Abramovich et al., J. R. Statist. Soc. B, vol. 60, pp. 725-749, 1998, describes a variation on this process, wherein a threshold is set to the wavelet coefficients. The above papers are incorporated herein by reference.